Details

sample104.0ms

Algorithm

intervals

Results

39.0ms	819×	body	80	nan
15.0ms	290×	body	80	valid

simplify9.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
7	2855
6	1644
5	941
4	490
3	203
2	76
1	27
0	13

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize91.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- a (/ 1.0 3.0)) 9.0)
0.1b	(fma (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
0.1b	(sqrt (* (- a (/ 1.0 3.0)) 9.0))
0.2b	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))

rewrite218.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt`
13×	`times-frac`
9×	`pow1`
8×	`add-cbrt-cube` `add-exp-log`
6×	`associate-l` `associate-*l/`
5×	`sqrt-prod`
4×	`expm1-log1p-u` `associate-/r*` `sqrt-div` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `associate-r` `flip--` `associate-/l*`
2×	`sqrt-pow1` `pow-prod-down` `associate-/r/` `difference-of-squares`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `pow1/2` `div-exp` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 89

Calls

4 calls:

111.0ms	(* (- a (/ 1.0 3.0)) 9.0)
2.0ms	(fma (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
46.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))
49.0ms	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))

series617.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (- a (/ 1.0 3.0)) 9.0)
179.0ms	(fma (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
114.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))
258.0ms	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))

simplify3.3s

Counts

101 → 101

Iterations

Iter	Nodes
done	5001
2	1720
1	549
0	231

prune1.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize76.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- a (/ 1.0 3.0)))
0.1b	(fma (/ rand (* (sqrt (- a (/ 1.0 3.0))) (sqrt 9.0))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
0.2b	(/ rand (* (sqrt (- a (/ 1.0 3.0))) (sqrt 9.0)))
0.3b	(* (sqrt (- a (/ 1.0 3.0))) (sqrt 9.0))

rewrite201.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
19×	`sqrt-prod`
15×	`*-un-lft-identity`
11×	`add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
9×	`pow1` `associate-l`
6×	`sqrt-div` `associate-r`
5×	`times-frac`
4×	`expm1-log1p-u` `associate-*l/` `insert-posit16` `log1p-expm1-u` `add-log-exp` `difference-of-squares` `unswap-sqr`
3×	`sqrt-pow1` `flip3--` `pow1/2` `pow-prod-down` `flip--` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `distribute-lft-out--`
1×	`rem-sqrt-square` `clear-num` `associate-/r` `frac-2neg` `sqrt-unprod` `-commutative` `fma-udef` `div-inv`

Counts

4 → 96

Calls

4 calls:

54.0ms	(sqrt (- a (/ 1.0 3.0)))
2.0ms	(fma (/ rand (* (sqrt (- a (/ 1.0 3.0))) (sqrt 9.0))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
48.0ms	(/ rand (* (sqrt (- a (/ 1.0 3.0))) (sqrt 9.0)))
92.0ms	(* (sqrt (- a (/ 1.0 3.0))) (sqrt 9.0))

series750.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(sqrt (- a (/ 1.0 3.0)))
248.0ms	(fma (/ rand (* (sqrt (- a (/ 1.0 3.0))) (sqrt 9.0))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
313.0ms	(/ rand (* (sqrt (- a (/ 1.0 3.0))) (sqrt 9.0)))
137.0ms	(* (sqrt (- a (/ 1.0 3.0))) (sqrt 9.0))

simplify3.2s

Counts

108 → 108

Iterations

Iter	Nodes
done	5003
2	1652
1	550
0	230

prune1.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize82.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- a (/ 1.0 3.0)))
0.1b	(fma (/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0)) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
0.2b	(/ rand (sqrt (- a (/ 1.0 3.0))))
0.2b	(/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))

rewrite290.0ms

Algorithm

rewrite-expression-head

Rules

440×	`times-frac`
334×	`add-sqr-sqrt`
258×	`sqrt-prod`
255×	`*-un-lft-identity`
203×	`add-cube-cbrt`
52×	`difference-of-squares`
36×	`associate-/l*`
26×	`distribute-lft-out--`
18×	`sqrt-div`
16×	`associate-/r/`
15×	`associate-/r*`
11×	`add-cbrt-cube` `add-exp-log`
9×	`flip3--` `div-inv` `flip--`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef` `associate-/l/`

Counts

4 → 343

Calls

4 calls:

46.0ms	(sqrt (- a (/ 1.0 3.0)))
2.0ms	(fma (/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0)) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
58.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
105.0ms	(/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))

series716.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(sqrt (- a (/ 1.0 3.0)))
235.0ms	(fma (/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0)) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
153.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
279.0ms	(/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))

simplify4.9s

Counts

355 → 355

Iterations

Iter	Nodes
done	5011
2	2908
1	1214
0	514

prune3.5s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize75.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ rand (* (cbrt (sqrt 9.0)) (cbrt (sqrt 9.0))))
0.3b	(/ 1 (sqrt (- a (/ 1.0 3.0))))
0.3b	(* (/ rand (* (cbrt (sqrt 9.0)) (cbrt (sqrt 9.0)))) (/ (/ 1 (sqrt (- a (/ 1.0 3.0)))) (cbrt (sqrt 9.0))))
0.4b	(/ (/ 1 (sqrt (- a (/ 1.0 3.0)))) (cbrt (sqrt 9.0)))

rewrite788.0ms

Algorithm

rewrite-expression-head

Rules

1271×	`times-frac`
943×	`add-sqr-sqrt`
666×	`*-un-lft-identity`
589×	`sqrt-prod`
532×	`add-cube-cbrt`
422×	`cbrt-prod`
301×	`associate-r`
122×	`difference-of-squares`
82×	`add-exp-log`
61×	`distribute-lft-out--`
40×	`sqrt-div` `associate-/r/`
39×	`associate-/l*`
38×	`div-exp`
36×	`add-cbrt-cube`
32×	`unswap-sqr`
24×	`div-inv`
21×	`cbrt-undiv` `prod-exp`
20×	`flip3--` `flip--`
19×	`associate-/r*`
13×	`cbrt-unprod`
8×	`pow1`
7×	`associate-l`
5×	`rec-exp` `1-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `pow-flip`
1×	`frac-times` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `inv-pow` `associate-/l/`

Counts

4 → 824

Calls

4 calls:

15.0ms	(/ rand (* (cbrt (sqrt 9.0)) (cbrt (sqrt 9.0))))
33.0ms	(/ 1 (sqrt (- a (/ 1.0 3.0))))
386.0ms	(* (/ rand (* (cbrt (sqrt 9.0)) (cbrt (sqrt 9.0)))) (/ (/ 1 (sqrt (- a (/ 1.0 3.0)))) (cbrt (sqrt 9.0))))
111.0ms	(/ (/ 1 (sqrt (- a (/ 1.0 3.0)))) (cbrt (sqrt 9.0)))

series1.5s

Counts

4 → 12

Calls

4 calls:

694.0ms	(/ rand (* (cbrt (sqrt 9.0)) (cbrt (sqrt 9.0))))
86.0ms	(/ 1 (sqrt (- a (/ 1.0 3.0))))
328.0ms	(* (/ rand (* (cbrt (sqrt 9.0)) (cbrt (sqrt 9.0)))) (/ (/ 1 (sqrt (- a (/ 1.0 3.0)))) (cbrt (sqrt 9.0))))
368.0ms	(/ (/ 1 (sqrt (- a (/ 1.0 3.0)))) (cbrt (sqrt 9.0)))

simplify6.0s

Counts

836 → 836

Iterations

Iter	Nodes
done	5003
1	2932
0	902

prune7.2s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes509.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	14
1	14
0	12

end0.0ms

sample5.1s

Algorithm

intervals

Results

3.1s	27544×	body	80	nan
640.0ms	9156×	body	80	valid